COMPLEX NUMBERS a) MCQS: 1. (2 + 3i)(1 – i) = 2. = A. 2 - 2i B. 2+ 4i C. 5 + i D.- 1+ i D. i 3. The imaginary part of i"(2 + V3i) – i(1- 2i) is: A. V3 – 1 4. The complex conjugate of (1- i) + (2i - 3)i is: C. 3 - 2i А. 1 A. -1 B. -i С. 1 B. 0 C. - V3 -1 D. - 4 A. -2-i B. 3 + 2i D. -1-2i 5. (V3 + i) (1 – v3i) = A. -i 7. If (3 – 2i)z - (7+4i) = 0, then z = B. -i С.i D. -1 2 B. 1 i 3. 2. D. 1 6. 2+i C. .+ -i 5 5 3. 3. 13 + B.+ 21 D. -+ 29 В. 3 C. 1+ 2i 13 13 -1+iV3 8. -1-iV3 A. -1- iv3 B. -(2 + iv3) C.(1 + iv3) D. -(1+ iv3) 9. Given that z --1+3i ,z+= = A. - + B- C-- D.-+ 12 i 4 В. 18 i 4 12 11 9 10. Given that Z1 = 1-i and z2 = 2 +i, z;- Z2 4 A. 2 B-i C.-2i D. 4 5 11. Given that z and z are conjugate complex numbers, which one of the following is not alway true? A. Re (z) = Re(7) B. Im (z) + Im(2) 0 C. Re (2) = Im(2) D. (z) = (7) 12. The roots of the equation: z-6z+ 34 = 0 are A. -2, 8 B. 6-10i, 6 + 10i C.-4, 16 D. 3-5i, 3 + 5i 13. The quadratic equation with 2-i as one of its roots is: B. x - 5x + 4 = 0 C. x-4x + 4 0 14. p+ 2 is a root of x2-x+q = 0. The values of p and q are: A. x* + 5x - 4 = 0 D. x² - 4x - 5 = (0 17 A. B. p = 1, q = 5 17 C. p=, 4 D. p= 4 15. Given that 5(a+ ib) +3-2i = 6i, the values of a and b are: 17 4 3 B. a = 5' A. a = -3, b = 8 C. a =, b D. a 5' 8 5' 16. If 3-i (x + iy), the values of x and y are: 1+2i 10 A. x = B. x = 7, y= 7 C. x = 7, y= -7 D. x = -7, y = 7 y 10 17. The complex number -2 + 2i can also be expressed as A. 2 [cos (-) + i sin (-) C. 2V2 [cos () 18. Find the modulus sroument form of the complex number: z = . B. 2 (co8 () + isin () +i sin () D. 2V2 cos (-)+ i sin (-) 4 A. A. 2 cos + i sm B, 2[cos -sinc 2{cos+1sin p. z [cos-i sin -V3 - i 5T 5T COS 74
COMPLEX NUMBERS a) MCQS: 1. (2 + 3i)(1 – i) = 2. = A. 2 - 2i B. 2+ 4i C. 5 + i D.- 1+ i D. i 3. The imaginary part of i"(2 + V3i) – i(1- 2i) is: A. V3 – 1 4. The complex conjugate of (1- i) + (2i - 3)i is: C. 3 - 2i А. 1 A. -1 B. -i С. 1 B. 0 C. - V3 -1 D. - 4 A. -2-i B. 3 + 2i D. -1-2i 5. (V3 + i) (1 – v3i) = A. -i 7. If (3 – 2i)z - (7+4i) = 0, then z = B. -i С.i D. -1 2 B. 1 i 3. 2. D. 1 6. 2+i C. .+ -i 5 5 3. 3. 13 + B.+ 21 D. -+ 29 В. 3 C. 1+ 2i 13 13 -1+iV3 8. -1-iV3 A. -1- iv3 B. -(2 + iv3) C.(1 + iv3) D. -(1+ iv3) 9. Given that z --1+3i ,z+= = A. - + B- C-- D.-+ 12 i 4 В. 18 i 4 12 11 9 10. Given that Z1 = 1-i and z2 = 2 +i, z;- Z2 4 A. 2 B-i C.-2i D. 4 5 11. Given that z and z are conjugate complex numbers, which one of the following is not alway true? A. Re (z) = Re(7) B. Im (z) + Im(2) 0 C. Re (2) = Im(2) D. (z) = (7) 12. The roots of the equation: z-6z+ 34 = 0 are A. -2, 8 B. 6-10i, 6 + 10i C.-4, 16 D. 3-5i, 3 + 5i 13. The quadratic equation with 2-i as one of its roots is: B. x - 5x + 4 = 0 C. x-4x + 4 0 14. p+ 2 is a root of x2-x+q = 0. The values of p and q are: A. x* + 5x - 4 = 0 D. x² - 4x - 5 = (0 17 A. B. p = 1, q = 5 17 C. p=, 4 D. p= 4 15. Given that 5(a+ ib) +3-2i = 6i, the values of a and b are: 17 4 3 B. a = 5' A. a = -3, b = 8 C. a =, b D. a 5' 8 5' 16. If 3-i (x + iy), the values of x and y are: 1+2i 10 A. x = B. x = 7, y= 7 C. x = 7, y= -7 D. x = -7, y = 7 y 10 17. The complex number -2 + 2i can also be expressed as A. 2 [cos (-) + i sin (-) C. 2V2 [cos () 18. Find the modulus sroument form of the complex number: z = . B. 2 (co8 () + isin () +i sin () D. 2V2 cos (-)+ i sin (-) 4 A. A. 2 cos + i sm B, 2[cos -sinc 2{cos+1sin p. z [cos-i sin -V3 - i 5T 5T COS 74
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter8: Polar Coordinates And Parametric Equations
Section8.3: Polar Form Of Complex Numbers; De Moivre's Theorem
Problem 3E
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Question
100%
Solve Q16, 17, 18 explaining detailly each step
Transcribed Image Text:COMPLEX NUMBERS
a) MCQS:
1. (2+3i)(1 – i) =
2. i =
A. 2 – 2i
B. 2+ 4i C. 5 + i D. – 1+ i
%3D
A. -1 B. -i
С. 1
D. i
3. The imaginary part of i"(2 + V3i) – i(1 – 2i) is: A. V3 –1 B. 0 C. - V3 -1 D. - 4
4. The complex conjugate of (1- i) + (2i - 3)i is:
A. -2 -i B. 3 + 2i
5. (V3 + i) + (1 – V3i) =
C. 3 – 2i D. -1-2i
А. 1
B. -i
C. i D. -1
D. +
2
1.
A. - -- L
5
2. 1
i
C. .=+
3
3
1
6.
2+i
2
B.
-
3 3
5 5
7. If (3 – 2i)z - (7 + 4i) = 0, then z =
A. +
13
26
29
B.+ 2i
29
2
C. 1+ 2i D.
-
-_re
13
13
-1+iv3
8.
-1-iv3
A. -1- iv3
B. -(2 + iv/3)
C. - (1+ iv3)
D. –(1+ iv3)
|
-
2
2
9. Given that z
2
--1+3i, z+
A. -- B- C-- D-+
12
4
В.
18
4
C.-
12
7
11
5
5
3
10. Given that Z1
= 1 -i and z = 2 + i, z;-=
Z.2
4
A.
5
2
4.
B.
5
2
3.
C.
5
2
i
5
8.
+ - i
D.
5
5
11. Given that z and Z are conjugate complex numbers, which cne of the following is not always
true?
A. Re (z) = Re(2) B. Im (z) + Im(2) = 0 C. Re(2) = Im(z) D. (z)
12. The roots cf the equation: z- 6z+ 34 = 0 are
A. -2, 8 B. 6- 10i, 6 + 10i C. -4, 16 D. 3 - 5i, 3 + 5i
13. The quadratic equation with 2 -i as one of its roots is:
A. x+ 5x – 4 0 B. x- 5x + 4= 0 C. x - 4x + 4 = 0
14. p+ 2 is a root of x-x+ 0. The values of p and q are:
(z)
D. x² - 4x – 5 = (0
%3D
17
A. p=
B. p = 1, q = 5
4.
1
17
C. p
15. Given that 5(a + ib) +3 - 2i = 6i, the values of a and b are:
D. p =, G = "
17
2
A. a = -3, b -8
B. a =
8.
5'
3
C. a =, b = =
3
С.а
a =, b =
8.
5
1
2
1
16. If
(x + iy), the values of x and y are:
|
3-i
1+2i
10
7.
A. x =
B. x = 7, y= 7 C. x 7, y = -7 D. x = -7, y = 7
10
10
17. The complex number -2 + 2i can also be expressed as
A. 2 [cos (-) + i sin (-ĐI
A. 2 cos (-)+ i sin
B. 2 cos () + i sin
+ i sin () D. 2V2 cos (-) + i sin (-|
TT
OS
C. 2v2 fcos () + i sin ( D.2V2 (cos (-) + isin(-)
3T
4
4
4
18. Find the modulus sroument form of the complex number: z = -V3 - i
A. A. 2 [cos +i sm B. z [cos-1sinc 2 cost -i sin
TT
[ca:
COS
COS
+ i sinD. 2 cos-
i sin
5TT
74
IN
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